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Hands-On Data Structures and Algorithms with Python – Third Edition
Hands-On Data Structures and Algorithms with Python – Third Edition

Hands-On Data Structures and Algorithms with Python – Third Edition: Store, manipulate, and access data effectively and boost the performance of your applications , Third Edition

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Hands-On Data Structures and Algorithms with Python – Third Edition

Introduction to Algorithm Design

The objective of this chapter is to understand the principles of designing algorithms, and the importance of analyzing algorithms in solving real-world problems. Given input data, an algorithm is a step-by-step set of instructions that should be executed in sequence to solve a given problem.

In this chapter, we will also learn how to compare different algorithms and determine the best algorithm for the given use-case. There can be many possible correct solutions for a given problem, for example, we can have several algorithms for the problem of sorting n numeric values. So, there is no one algorithm to solve any real-world problem.

In this chapter, we will look at the following topics:

  • Introducing algorithms
  • Performance analysis of an algorithm
  • Asymptotic notation
  • Amortized analysis
  • Choosing complexity classes
  • Computing the running time complexity of an algorithm

Introducing algorithms

An algorithm is a sequence of steps that should be followed in order to complete a given task/problem.

It is a well-defined procedure that takes input data, processes it, and produces the desired output. A representation of this is shown in Figure 2.1.

Figure 2.1: Introduction to algorithms

Summarized below are some important reasons for studying algorithms:

  • Essential for computer science and engineering
  • Important in many other domains (such as computational biology, economics, ecology, communications, ecology, physics, and so on)
  • They play a role in technology innovation
  • They improve problem-solving and analytical thinking

There are two aspects that are of prime importance in solving a given problem. Firstly, we need an efficient mechanism to store, manage, and retrieve data, which is required to solve a problem (this comes under data structures); secondly, we require an efficient algorithm that is a finite...

Performance analysis of an algorithm

The performance of an algorithm is generally measured by the size of its input data, n, and the time and the memory space used by the algorithm. The time required is measured by the key operations to be performed by the algorithm (such as comparison operations), where key operations are instructions that take a significant amount of time during execution. Whereas the space requirement of an algorithm is measured by the memory needed to store the variables, constants, and instructions during the execution of the program.

Time complexity

The time complexity of the algorithm is the amount of time that an algorithm will take to execute on a computer system to produce the output. The aim of analyzing the time complexity of the algorithm is to determine, for a given problem and more than one algorithm, which one of the algorithms is the most efficient with respect to the time required to execute. The running time required by an algorithm depends...

Asymptotic notation

To analyze the time complexity of an algorithm, the rate of growth (order of growth) is very important when the input size is large. When the input size becomes large, we only consider the higher-order terms and ignore the insignificant terms. In asymptotic analysis, we analyze the efficiency of algorithms for large input sizes considering the higher order of growth and ignoring the multiplicative constants and lower-order terms.

We compare two algorithms with respect to input size rather than the actual runtime and measure how the time taken increases with an increased input size. The algorithm which is more efficient asymptotically is generally considered a better algorithm as compared to the other algorithm. The following asymptotic notations are commonly used to calculate the running time complexity of an algorithm:

  • θ notation: It denotes the worst-case running time complexity with a tight bound.
  • Ο notation: It denotes the...

Amortized analysis

In the amortized analysis of an algorithm, we average the time required to execute a sequence of operations with all the operations of the algorithm. This is called amortized analysis. Amortized analysis is important when we are not interested in the time complexity of individual operations but we are interested in the average runtime of sequences of operations. In an algorithm, each operation requires a different amount of time to execute. Certain operations require significant amounts of time and resources while some operations are not costly at all. In amortized analysis, we analyze algorithms considering both the costly and less costly operations in order to analyze all the sequences of operations. So, an amortized analysis is the average performance of each operation in the worst case considering the cost of the complete sequence of all the operations. Amortized analysis is different from average-case analysis since the distribution of the input values is not...

Composing complexity classes

Normally, we need to find the total running time of complex operations and algorithms. It turns out that we can combine the complexity classes of simple operations to find the complexity class of more complex, combined operations. The goal is to analyze the combined statements in a function or method to understand the total time complexity of executing several operations. The simplest way to combine two complexity classes is to add them. This occurs when we have two sequential operations. For example, consider the two operations of inserting an element into a list and then sorting that list. Assuming that inserting an item occurs in O(n) time, and sorting in O(nlogn) time, then we can write the total time complexity as O(n + nlogn); that is, we bring the two functions inside the O(…), as per Big O computation. Considering only the highest-order term, the final worst-case complexity becomes O(nlogn).

If we repeat an operation, for example in...

Computing the running time complexity of an algorithm

To analyze an algorithm with respect to the best-, worst-, and average-case runtime of the algorithm, it is not always possible to compute these for every given function or algorithm. However, it is always important to know the upper-bound worst-case runtime complexity of an algorithm in practical situations; therefore, we focus on computing the upper-bound Big O notation to compute the worst-case runtime complexity of an algorithm:

  1. Find the worst-case runtime complexity of the following Python snippet:
    # loop will run n times
    for i in range(n):
        print("data")  #constant time
    

    Solution: The runtime for a loop, in general, takes the time taken by all statements in the loop, multiplied by the number of iterations. Here, total runtime is defined as follows:

    T(n) = constant time (c) * n = c*n = O(n)

  1. Find the time complexity of the following Python snippet: ...

Summary

In this chapter, we have looked at an overview of algorithm design. The study of algorithms is important because it trains us to think very specifically about certain problems. It is conducive to increasing our problem-solving abilities by isolating the components of a problem and defining the relationships between them. In this chapter, we discussed different methods for analyzing algorithms and comparing algorithms. We also discussed asymptotic notations, namely: Big Ο, Ω, and θ notation.

In the next chapter, we will discuss algorithm design techniques and strategies.

Exercises

  1. Find the time complexity of the following Python snippets:
  1. i=1
    while(i<n):
        i*=2
        print("data")
    
  2. i =n
    while(i>0):
        print('complexity')
        i/ = 2
    
  3. for i in range(1,n):
        j = i
        while(j<n):
            j*=2
    
  4. i=1
    while(i<n):
        print('python')
            i = i**2
    

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Key benefits

  • Explore functional and reactive implementations of traditional and advanced data structures
  • Apply a diverse range of algorithms in your Python code
  • Implement the skills you have learned to maximize the performance of your applications

Description

Choosing the right data structure is pivotal to optimizing the performance and scalability of applications. This new edition of Hands-On Data Structures and Algorithms with Python will expand your understanding of key structures, including stacks, queues, and lists, and also show you how to apply priority queues and heaps in applications. You’ll learn how to analyze and compare Python algorithms, and understand which algorithms should be used for a problem based on running time and computational complexity. You will also become confident organizing your code in a manageable, consistent, and scalable way, which will boost your productivity as a Python developer. By the end of this Python book, you’ll be able to manipulate the most important data structures and algorithms to more efficiently store, organize, and access data in your applications.

Who is this book for?

This book is for developers and programmers who are interested in learning about data structures and algorithms in Python to write complex, flexible programs. Basic Python programming knowledge is expected.

What you will learn

  • Understand common data structures and algorithms using examples, diagrams, and exercises
  • Explore how more complex structures, such as priority queues and heaps, can benefit your code
  • Implement searching, sorting, and selection algorithms on number and string sequences
  • Become confident with key string-matching algorithms
  • Understand algorithmic paradigms and apply dynamic programming techniques
  • Use asymptotic notation to analyze algorithm performance with regard to time and space complexities
  • Write powerful, robust code using the latest features of Python
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Publication date : Jul 29, 2022
Length: 496 pages
Edition : 3rd
Language : English
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Table of Contents

15 Chapters
Python Data Types and Structures Chevron down icon Chevron up icon
Introduction to Algorithm Design Chevron down icon Chevron up icon
Algorithm Design Techniques and Strategies Chevron down icon Chevron up icon
Linked Lists Chevron down icon Chevron up icon
Stacks and Queues Chevron down icon Chevron up icon
Trees Chevron down icon Chevron up icon
Heaps and Priority Queues Chevron down icon Chevron up icon
Hash Tables Chevron down icon Chevron up icon
Graphs and Algorithms Chevron down icon Chevron up icon
Searching Chevron down icon Chevron up icon
Sorting Chevron down icon Chevron up icon
Selection Algorithms Chevron down icon Chevron up icon
String Matching Algorithms Chevron down icon Chevron up icon
Other Books You May Enjoy Chevron down icon Chevron up icon
Index Chevron down icon Chevron up icon

Customer reviews

Top Reviews
Rating distribution
Full star icon Full star icon Full star icon Full star icon Half star icon 4.8
(26 Ratings)
5 star 80.8%
4 star 15.4%
3 star 3.8%
2 star 0%
1 star 0%
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MLEngineer Jan 10, 2023
Full star icon Full star icon Full star icon Full star icon Full star icon 5
This book strikes the ideal balance between mathematical algorithm theory and coding. There are many-a-book with only theory and a lot of coding sources with very little in terms of explanation/theory.This is a very good book that mixes both. I myself invent/develop algorithms and appreciate very much this book's balanced approach.
Amazon Verified review Amazon
v Oct 18, 2022
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Most data structure and algorithm book/video have been written/taught using C/C++ or Java in the market. For many python only beginner, epecially in data science/machine leanring, a python version data structure and algorithm book can be a great reference to study high quality programming systemetically, This book fills the gap of the demand. Good job!
Amazon Verified review Amazon
Siddhant Kochrekar Apr 23, 2023
Full star icon Full star icon Full star icon Full star icon Full star icon 5
While writing production level code, I have encountered many situations where the efficiency of the chosen data structure or algorithm has a significant impact on the performance of the system. I was particularly interested in reviewing this book, as it aims to provide an introduction to the essential topics and extend into practical applications for each of them.It focuses both on theoretical concepts and the practical applications. The simple examples shown in the book are suitable for beginners and the complex problems are framed in such a way that even the experienced developers would benefit. This book assumes a basic level of knowledge in Python programming. In particular, the book could have included generators, decorators, and meta-classes, to showcase how these concepts can be used to implement more efficient data structures and algorithms.The book does provide valuable insights into various data structures and algorithms. The author's explanations of the concepts are clear and concise, and the code examples are well-structured and easy to understand. The book covers a wide range of topics, including linked lists, trees, graphs, and sorting algorithms, making it a comprehensive resource for beginners. Overall it is a useful starting point for beginners who are new to data structures and algorithms and want to use Python as the programming language.
Amazon Verified review Amazon
David M. Mar 19, 2023
Full star icon Full star icon Full star icon Full star icon Full star icon 5
In this book, the author presented the concept of complex data structures and algorithms in a systematic way with clean examples that can be read and understood by readers and learners having various backgrounds, as for example CS, IT, Business or other quantitative and analytical fields. This book will be useful not only for developers, but also data scientists and data engineers as well.
Amazon Verified review Amazon
Agni Oct 18, 2022
Full star icon Full star icon Full star icon Full star icon Full star icon 5
The Author demonstrates a fresh look at the subject!I have instructed the course at the University for some time and I loved reading it. I think there are many similar books, but none go to the depths and clarity that this one does. Especially, I liked that fact that the author actually demonstrates all the concepts with examples, and also puts it in tabular format for easy reference.This will be a great asset to have, both for the beginner and for the advanced learner.Enjoy learning!
Amazon Verified review Amazon
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